In this paper, we describe the development of a novel instrument, tentatively called tomographic Mueller-matrix scatterometer (TMS), which enables illuminating sequentially a sample by a plane wave with varying illumination directions and recording, for each illumination, the polarized scattered field along various directions of observation in the form of scattering Mueller matrices. The incidence angle is varied from 0° to 65.6° with the rotation of a flat mirror that changes the position of the focal point of a light beam on the back focal plane of a high numerical aperture objective lens. The scattering Mueller matrices are collected over a wide range of scattering angles (0°-67°) and azimuthal angles (0°-360°). The developed instrument was then applied for the measurement of nanostructures in combination with an inverse scattering problem solving technique. The experiment performed on a periodic nanostructure preliminarily demonstrates the performance of TMS as well as its potential in nanostructure metrology. It is expected that the TMS would be a powerful tool for characterizing the polarized scattered-field distributions and measuring nanostructures in nanomanufacturing.